Classical Mechanics Illustrated by Modern Physics

by Guery-odelin, David; Lahaye, Thierry

• ISBN13: 9781848164802
• ISBN10: 1848164807
• Format: Paperback
• Copyright: 2010-12-30
• Publisher: Imperial College Pr

Summary

In many fields of modern physics, classical mechanics plays a key role. However, the teaching of mechanics at the undergraduate level often confines the applications to old-fashioned devices such as combinations of springs and masses, pendulums, or rolling cylinders. This book provides an illustration of classical mechanics in the form of problems (at undergraduate level) inspired - for the most part - by contemporary research in physics, and resulting from the teaching and research experience of the authors. A noticeable feature of this book is that it emphasizes the experimental aspects of a large majority of problems. All problems are accompanied by detailed solutions: the calculations are clarified and their physical significance commented on in-depth. Within the solutions, the basic concepts from undergraduate lectures in classical mechanics, necessary to solve the problems, are recalled when needed. the authors systematically mention recent bibliographical references (most of them freely accessible via the Internet) allowing the reader to deepen their understanding of the subject, and thus contributing to the building of a general culture in physics.

Table of Contents

Foreword	p. v
Preface	p. vii
Acknowledgments	p. ix
Notations	p. xv
Orders of Magnitude and Dimensional Analysis	p. 1
A few orders of magnitude *	p. 1
Dimensional analysis *	p. 6
Motion in the Gravity Field	p. 13
Safety parabola *	p. 13
Shape of a liquid jet *	p. 15
The tautochrone curve **	p. 18
Gravitational cavity **	p. 22
Friction	p. 29
Energy balance for forced oscillations *	p. 29
Solid friction versus fluid friction *	p. 32
Fluid friction and delayed response **	p. 37
Absence of dissipation in a system with friction **	p. 40
Rotating Frames	p. 45
The rotating saddle *	p. 45
When Coriolis enters the game *	p. 49
Oscillators	p. 57
Oscillation period **	p. 57
Optimal transport of a bunch of atoms **	p. 63
Trajectory in a curved guide**	p. 69
Role of non-linearities ***	p. 72
A Few Theorems in Mechanics	p. 81
The virial theorem **	p. 81
Adiabatic invariants ***	p. 85
Lax form and constants of motion ***	p. 91
Collisions	p. 101
Collisions and thermalization *	p. 101
Minimum distance of approach *	p. 105
Landau's criterion of superfluidity **	p. 106
Collision cross section **	p. 110
Slowing atoms with a moving wall **	p. 125
Manipulation of Charged Particles	p. 135
Coulomb crystal *	p. 135
Normal modes of a one-dimensional ion chain **	p. 138
Monopole mode for interacting particles **	p. 146
Mass spectrometry **	p. 149
Ponderomotive force **	p. 161
Effective potential and phase jump **	p. 167
ôColdö Atoms	p. 173
Effusive atomic beam **	p. 174
Zeeman slower **	p. 180
Doppler cooling **	p. 188
Time-of-flight thermometry **	p. 197
Linear and parametric heating ***	p. 200
Evaporative cooling *	p. 207
Celestial Mechanics	p. 213
Closed trajectories in a central field *	p. 213
Lagrange points ***	p. 215
Relativistic Mechanics	p. 229
On the other side of the Galaxy *	p. 229
Relativistic oscillator **	p. 232
Perihelion precession of Mercury **	p. 235
Electron motion in a plane wave ***	p. 239
Index	p. 247
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